No, because this an example of an invariant plural, as we see in fish or sheep, in deer or caribou or elk or moose, or in pronghorn or antelope, and so on and so forth:
- One buffalo, two buffalo, a herd of buffalo.
- One bison, two bison, a herd of bison.
- One deer, two deer, a herd of deer.
- One caribou, two caribou, a herd of caribou.
- One elk, two elk, a herd of elk.
- One moose, two moose, a herd of moose.
- One pronghorn, two pronghorn, a herd of pronghorn.
- One antelope, two antelope, a herd of antelope.
You can tell from the lack of determiner that it’s a group of them used in the general sense, which is reinforced by having both verbs in the plural as well.
The word buffalo was specifically chosen for this silly little ditty because the plural noun looks just like the plural verb, which is not usually the way these things work. (Sometimes water buffaloes are inflected into the plural regularly, but when speaking of bison, such “buffalo” usually are not.)
You couldn’t do it with some city named Hound or Cow since you would end up with a different plural noun like “Hound hounds hounding Hound hounds.”
But you could do it with a city named Fish (if you could find one!), since then you’d have “Fish fish fishing Fish fish.”